Math, Sleeves and Xah in Second Life
![polyhedron n nekos](i/sl_math/polyhedron_n_nekos.jpg)
![polyhedron n nekos 2](i/sl_math/polyhedron_n_nekos_2.jpg)
![Truchet tiles](i/sl_math/Truchet_tiles.jpg)
For a 3D version by Sleeves, see: Celtic Knots, Truchet tiles, Combinatorial Patterns.
![hyperbolic paraboloid](http://xahlee.info/surface/hyperbolic-paraboloid/hyperbolic_paraboloid_sl.jpg)
It is called hyperbolic-paraboloid because the horizontal cross sections are hyperbolas and diagonal vertical cross-sections are parabolas. This structure is commonly used as roofs for modern pavillions.
You can easily make a hyperbolic-paraboloid. Imagine a cube. Mark the top two opposite corners. These two corners will be the top two vertexes of the surface you see in the above image. Now, also mark the two opposite corners at the bottom of the cube. Draw diagonal lines from these corners. (look at the figure above. Your diagonal lines will be the edges of the surface) Mark regular intervals on these diagonal lines. Now, connect lines from one diagonal to the other side. You are all done!
For a Java applet that does live rotation of hyperbolic-paraboloid, see hyperbolic-paraboloid.
![tiling dragon](i/sl_math/tiling_dragon.jpg)
Lorenz Attractor
Visualization of the math non-linear dynamic system called Lorenz attractor.
![math lorenz attractor 020](i/sl_math/math_lorenz_attractor_020.png)
![math lorenz attractor 015](i/sl_math/math_lorenz_attractor_015.png)
![math lorenz attractor 002](i/sl_math/math_lorenz_attractor_002.png)
![sl lorenz attractor](i/sl_math/sl_lorenz_attractor.jpg)